The square root of 961 is expressed as √961 in the radical form and as (961)½ or (961)0.5 in the exponent form. The square root of 961 is 31. It is the positive solution of the equation x2 = 961. The number 961 is a perfect square.

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Square Root of 961: 31Square Root of 961 in exponential form: (961)½ or (961)0.5Square Root of 961 in radical form: √961

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1.What is the Square Root of 961?
2.How to find the Square Root of 961?
3.Is the Square Root of 961 Rational?
4.FAQs

The square root of 961, (or root 961), is the number which when multiplied by itself gives the product as 961. Therefore, the square root of 961 = √961 = 31.

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Value of √961 by Long Division Method

Explanation:

Forming pairs: 09 and 61Find a number Y (3) such that whose square is Bring down the next pair 61, to the right of the remainder 0. The new dividend is now 61.Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 1) such that 6Z × Z Divide 61 by 61 with the quotient as 1, giving the remainder = 61 - 61 × 1 = 61 - 61 = 0.We stop the process since the remainder is now 0 and there are no more digits that can be brought down.

Therefore, the square root of 961 by long division method is 31.


Is Square Root of 961 Rational?


The value of √961 is 31. Hence, the square root of 961 is a rational number.

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Square Root of 961 Solved Examples


Example 1: Solve the equation x2 − 961 = 0

Solution:

x2 - 961 = 0 i.e. x2 = 961x = ±√961Since the value of the square root of 961 is 31,⇒ x = +√961 or -√961 = 31 or -31.


Example 3: If the area of a circle is 961π in2. Find the radius of the circle.

Solution:

Let "r" be the radius of the circle.⇒ Area of the circle = πr2 = 961π in2⇒ r = ±√961 inSince radius can"t be negative,⇒ r = √961Square root of 961 is 31.⇒ r = 31 in


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FAQs on the Square Root of 961

What is the Value of the Square Root of 961?

The square root of 961 is 31.

Why is the Square Root of 961 a Rational Number?

Upon prime factorizing 961 i.e. 312, we find that all the prime factors are in even power. This implies that the square root of 961 is a positive integer. Therefore, the square root of 961 is rational.

What is the Square Root of -961?

The square root of -961 is an imaginary number. It can be written as √-961 = √-1 × √961 = i √961 = 31iwhere i = √-1 and it is called the imaginary unit.

If the Square Root of 961 is 31. Find the Value of the Square Root of 9.61.

See more: Closed Circle On A Number Line, Basic Linear Inequalities

Let us represent √9.61 in p/q form i.e. √(961/100) = 9.61/10 = 3. Hence, the value of √9.61 = 3

What is the Square Root of 961 in Simplest Radical Form?

We need to express 961 as the product of its prime factors i.e. 961 = 31 × 31 . Therefore, as visible, the radical form of the square root of 961 cannot be simplified further. Therefore, in the simplest radical form of the square root of 961 can be written as √961.

Evaluate 5 plus 10 square root 961

The given expression is 5 + 10 √961. We know that the square root of 961 is 31. Therefore, 5 + 10 √961 = 5 + 10 × 31 = 5 + 310 = 315